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The announcement of Mr. Boehner’s new game plan has been months in the making. It was at the heart of the debt-ceiling deal last month that allowed the federal government to borrow an unlimited amount of money through mid-May in exchange for forcing Senate Democrats to write a budget for the first time in four years. Last week, Mr. Boehner also called on Senate Democrats to offer a proposal to cancel and replace the $85 billion in spending cuts — know as sequesters — that were triggered by the 2011 debt deal.

Speaking to reporters late last week, Mr. Boehner said that if Mr. Obama is “serious about enacting his agenda, I think it must start with the part of this Congress that his party controls, the United States Senate.”

“What can he get passed in the United States Senate?” Mr. Boehner said, arguing the president’s agenda is out of touch with most Americans. “And I think many in the president’s own party won’t support those ideas.”